A dynamic non-uniform segmentation method for first-order polynomial function evaluation

Abstract

This paper presents a new dynamic non-uniform segmentation method for the first-order polynomial function evaluation. The proposed method can evaluate the elementary functions (e.g. log, exp, sin, cos, tan, etc.) and combinations of these functions by an optimized linear approximation with the fewest non-uniform segments. Compared with the previous evaluation method based on the static bit-width analysis, the proposed method is mainly based on a dynamic bit-width analysis and capable of reducing the number of segments, which in turn can significantly reduce the memory size occupied in hardware. The proposed dynamic method can evaluate the function to satisfy accuracy by the linear approximation in which the input, coefficients, and intermediate values are rounded to fewer bit-width, which cannot be achieved by previous static non-uniform segmentation methods. The hardware performance evaluation results on FPGA show that the proposed method consumes about 66% fewer hardware resources, 56% less actual memory usage, and performs 32% shorter delay on average in comparison with the non-uniform segmentation method based on static bit-width analysis.